Please explain the dynamics behind Agamemnon's taking of Achilles's girl Briseis.
Agamemnon was forced to return his war prize, Chryseis, to her father because of an oracle delivered through the seer Calchas. This made Agamemnon irate as he felt overpowered, manipulated and robbed of his rightful war spoil. In an (irrational) act of retaliation, Agamemnon demonstrates his own powerful authority and overpowers, manipulates and robs Achilles of his rightful war prize and spoil by taking Achilles's woman Briseis.
Achilles valued Briseis above all and was in his turn made irate by Agamemnon's blatant breaking of the laws of war spoil, by which he demonstrated the original "Because I can!": Agamemnon said, "that you may learn how much stronger I am than you are...."
As a result of this violation on Agamemnon's part, Achilles refused to fight on Agamemnon's behalf. Ironically, even though there was an element of bad tempered petulance behind Achilles's decision, he was right in that Agamemnon had forfeited Achilles allegiance by breaking the laws of fair gain and reward in war. Unfortunately, since Achilles was one of the mightiest champions fighting under Agamemnon, Achilles doomed his fellow warriors and especially his friend, Patroclus, to a dismal future.